# Loads data
load("bc_bear_occurrences.Rda")
load("BC_Covariates.Rda")
summary(DATA)
## Length Class Mode
## Window 1 SpatialPolygons S4
## Elevation 10 im list
## Forest 10 im list
## HFI 10 im list
## Dist_Water 10 im list
# Extracts location columns
bears_loc <- occ_data[, c("decimalLongitude", "decimalLatitude", "month", "year")]
bears_loc_filtered <- subset(bears_loc, year %in% c(2020, 2021, 2022, 2023, 2024))
# Creates sf object
bears_sf <- st_as_sf(
bears_loc_filtered,
coords = c("decimalLongitude", "decimalLatitude"),
crs = 4326 # WGS84 (longitude/latitude)
)
# BC Albers projection
bears_sf_proj <- st_transform(bears_sf, crs = 3005)
# Extracts coordinates
coords <- st_coordinates(bears_sf_proj)
# Extracts BC window
window_sf <- st_as_sf(DATA$Window)
window_proj <- st_transform(window_sf, crs = 3005)
window <- as.owin(window_proj)
# Creates ppp object
bears_ppp <- ppp(
x = coords[,1],
y = coords[,2],
window = window
)
## Warning: 187 points were rejected as lying outside the specified window
## Warning: data contain duplicated points
plot(bears_ppp, pch = 21, main = "Black bear occurrences in BC, 2024")
## Warning in plot.ppp(bears_ppp, pch = 21, main = "Black bear occurrences in BC,
## 2024"): 187 illegal points also plotted
# Defines the seasons and corresponding colors
seasons <- list(
winter = c(12, 1, 2),
spring = c(3, 4, 5),
summer = c(6, 7, 8),
autumn = c(9, 10, 11)
)
# Create an empty list to store the ppp objects for each season
ppp_list <- list()
# Create an empty list to store the filtered data for each season
bears_sf_list <- list()
# Loop over seasons
for (i in 1:length(seasons)) {
# Filter for each season
season_name <- names(seasons)[i]
season_months <- seasons[[i]]
# Filter bears_loc_filtered by the season's months
bears_loc_season <- bears_loc_filtered[bears_loc_filtered$month %in% season_months, ]
# Print the number of observations for this season
cat(season_name, ": ", nrow(bears_loc_season), " observations\n", sep="")
# Create sf object for the filtered season
bears_sf_season <- st_as_sf(
bears_loc_season,
coords = c("decimalLongitude", "decimalLatitude"),
crs = 4326 # WGS84 (longitude/latitude)
)
# Transform to BC Albers projection
bears_sf_season_proj <- st_transform(bears_sf_season, crs = 3005)
# Store sf object in the list
bears_sf_list[[season_name]] <- bears_sf_season_proj
# Extract x, y coordinates
coords <- st_coordinates(bears_sf_season_proj)
# Create ppp object for each season
suppressWarnings(
bears_ppp_season <- ppp(
x = coords[, 1],
y = coords[, 2],
window = window
)
)
# Store ppp object in the list
ppp_list[[season_name]] <- bears_ppp_season
}
## winter: 76 observations
## spring: 808 observations
## summer: 1862 observations
## autumn: 841 observations
# Plot the four maps in a 2x2 grid
par(mfrow=c(2,2), mar=c(1,1,1,1)) # Set up a 2x2 plotting window
# Loop over ppp objects and plot them
for (i in 1:length(ppp_list)) {
season_name <- names(ppp_list)[i]
suppressWarnings(
plot(ppp_list[[season_name]],
main = paste(season_name, "(2024)"),
pch = 21)
)
}
plot(DATA$Elevation)
plot(DATA$Forest)
plot(DATA$HFI)
plot(DATA$Dist_Water)
elev <- DATA$Elevation
cover <- DATA$Forest
dist_water <- DATA$Dist_Water
hfi <- DATA$HFI
# intensity as a function of elev
par(mfrow=c(2,2), mar=c(2,2,2,2))
for (i in 1:length(ppp_list)) {
season_name <- names(ppp_list)[i]
rho <- rhohat(ppp_list[[season_name]], elev)
plot(rho, xlim=c(0, max(elev)), main = paste(season_name))
}
# Loads elevation raster
elev <- DATA$Elevation
# Converts im to raster
im2raster <- function(im_obj) {
m <- as.matrix(im_obj)
r <- raster(m)
ext <- c(im_obj$xrange[1] - im_obj$xstep/2,
im_obj$xrange[2] + im_obj$xstep/2,
im_obj$yrange[1] - im_obj$ystep/2,
im_obj$yrange[2] + im_obj$ystep/2)
extent(r) <- ext
return(r)
}
elev_raster <- im2raster(elev)
# Extracts elevation values at occurrence locations
bears_sf_proj$elev_value <- extract(elev_raster, bears_sf_proj)
summary(bears_sf_proj$elev_value)
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 11.68 461.09 644.88 754.84 937.91 2308.18 1499
# KDE for Bear Locations
kde_b <- density(bears_sf_proj$elev_value, na.rm = TRUE, bw = "SJ-dpi")
summary(bears_sf_proj$elev_value)
## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 11.68 461.09 644.88 754.84 937.91 2308.18 1499
plot(kde_b,
main = "Kernel Density Estimate of Elevation at Bear Locations",
xlab = "Elevation (meters)",
ylab = "Density",
col = "#2C6B2F",
lwd = 2)
# NA with mean elevation
mean_elev <- mean(as.vector(as.matrix(elev)), na.rm = TRUE)
elev_clean <- eval.im(ifelse(is.na(elev), mean_elev, elev))
# model
elevation_model <- ppm(bears_ppp, ~ elev, covariates = list(elev = elev_clean))
print(elevation_model)
## Nonstationary Poisson process
## Fitted to point pattern dataset 'bears_ppp'
##
## Log intensity: ~elev
##
## Fitted trend coefficients:
## (Intercept) elev
## -17.36871576 -0.00253243
##
## Estimate S.E. CI95.lo CI95.hi Ztest
## (Intercept) -17.36871576 2.963479e-02 -17.426798885 -17.310632643 ***
## elev -0.00253243 4.234993e-05 -0.002615434 -0.002449426 ***
## Zval
## (Intercept) -586.09208
## elev -59.79774
# Predicts and plots intensity
pred_intensity_elev <- predict(elevation_model)
plot(pred_intensity_elev,
main = "Predicted Intensity Based on Elevation")
points(bears_ppp,
pch = 20,
cex = 0.4,
col = "#B24A2F")
elevation_residuals <- residuals(elevation_model, type = "pearson")
elevation_residuals$v[!is.finite(elevation_residuals$v)] <- NA
plot(elevation_residuals,
main = "Residuals - Elevation Model",
na.col = "transparent")
####All seasons show a negative relationship between bear occurrences and elevation. Winter has the largest negative coefficient (-0.0049), meaning a stronger decrease in occurrences with elevation.
# Seasonal elevation models
models_elev_seasonal <- list()
for (season in names(ppp_list)) {
models_elev_seasonal[[season]] <- ppm(ppp_list[[season]], ~ elev, covariates = list(elev = elev_clean))
cat("Model for", season, ":\n")
print(models_elev_seasonal[[season]])
}
## Warning: glm.fit: algorithm did not converge
## Model for winter :
## Nonstationary Poisson process
## Fitted to point pattern dataset 'ppp_list[[season]]'
##
## Log intensity: ~elev
##
## Fitted trend coefficients:
## (Intercept) elev
## -20.281500393 -0.004896402
##
## Estimate S.E. CI95.lo CI95.hi Ztest
## (Intercept) -20.281500393 0.1590970890 -20.593324958 -19.96967583 ***
## elev -0.004896402 0.0004162485 -0.005712234 -0.00408057 ***
## Zval
## (Intercept) -127.47876
## elev -11.76317
## *** Fitting algorithm for 'glm' did not converge ***
## Model for spring :
## Nonstationary Poisson process
## Fitted to point pattern dataset 'ppp_list[[season]]'
##
## Log intensity: ~elev
##
## Fitted trend coefficients:
## (Intercept) elev
## -18.938423756 -0.002390713
##
## Estimate S.E. CI95.lo CI95.hi Ztest
## (Intercept) -18.938423756 6.296883e-02 -19.061840399 -18.815007114 ***
## elev -0.002390713 8.708531e-05 -0.002561397 -0.002220029 ***
## Zval
## (Intercept) -300.75870
## elev -27.45254
## Model for summer :
## Nonstationary Poisson process
## Fitted to point pattern dataset 'ppp_list[[season]]'
##
## Log intensity: ~elev
##
## Fitted trend coefficients:
## (Intercept) elev
## -18.213839873 -0.002227723
##
## Estimate S.E. CI95.lo CI95.hi Ztest
## (Intercept) -18.213839873 4.265390e-02 -18.297439975 -18.13023977 ***
## elev -0.002227723 5.699771e-05 -0.002339437 -0.00211601 ***
## Zval
## (Intercept) -427.01468
## elev -39.08443
## Model for autumn :
## Nonstationary Poisson process
## Fitted to point pattern dataset 'ppp_list[[season]]'
##
## Log intensity: ~elev
##
## Fitted trend coefficients:
## (Intercept) elev
## -18.514156648 -0.003139775
##
## Estimate S.E. CI95.lo CI95.hi Ztest
## (Intercept) -18.514156648 5.671064e-02 -18.625307457 -18.403005838 ***
## elev -0.003139775 9.455484e-05 -0.003325099 -0.002954451 ***
## Zval
## (Intercept) -326.46708
## elev -33.20586
# Combines seasonal data
bears_all_elevation <- do.call(rbind, lapply(names(bears_sf_list), function(season) {
sf_season <- bears_sf_list[[season]]
coords <- st_coordinates(sf_season)
elev_vals <- extract(elev_raster, sf_season)
data.frame(x = coords[, 1], y = coords[, 2],
elev_value = elev_vals, season = season)
}))
bears_all_elevation$season <- as.factor(bears_all_elevation$season)
bears_all_elevation$count <- 1
# GAM with elevation and season
gam_elevation <- gam(count ~ s(elev_value) + season, data = bears_all_elevation, family = poisson())
summary(gam_elevation)
##
## Family: poisson
## Link function: log
##
## Formula:
## count ~ s(elev_value) + season
##
## Parametric coefficients:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 6.729e-17 4.510e-02 0 1
## seasonspring 2.172e-22 6.531e-02 0 1
## seasonsummer 7.375e-22 5.431e-02 0 1
## seasonwinter 8.153e-21 1.544e-01 0 1
##
## Approximate significance of smooth terms:
## edf Ref.df Chi.sq p-value
## s(elev_value) 1 1.001 0 1
##
## R-sq.(adj) = NaN Deviance explained = NaN%
## UBRE = -0.99521 Scale est. = 1 n = 2088
# Polynomial ppm model with season
bears_all_elevation <- ppp(
x = bears_all_elevation$x,
y = bears_all_elevation$y,
window = window,
marks = bears_all_elevation$season
)
## Warning: 187 points were rejected as lying outside the specified window
## Warning: data contain duplicated points
marks(bears_all_elevation) <- data.frame(season = marks(bears_all_elevation))
model_poly_elevation <- ppm(bears_all_elevation, ~ polynom(elev, 2) + marks,
covariates = list(elev = elev_clean))
print(model_poly_elevation)
## Nonstationary multitype Poisson process
## Fitted to point pattern dataset 'bears_all_elevation'
##
## Possible marks: 'autumn', 'spring', 'summer' and 'winter'
##
## Log intensity: ~elev + I(elev^2) + marks
##
## Fitted trend coefficients:
## (Intercept) elev I(elev^2) marksspring markssummer
## -1.850394e+01 -3.937116e-03 9.510112e-07 -3.957121e-02 7.891398e-01
## markswinter
## -2.379296e+00
##
## Estimate S.E. CI95.lo CI95.hi Ztest
## (Intercept) -1.850394e+01 4.652449e-02 -1.859513e+01 -1.841276e+01 ***
## elev -3.937116e-03 1.034097e-04 -4.139795e-03 -3.734437e-03 ***
## I(elev^2) 9.510112e-07 6.143974e-08 8.305915e-07 1.071431e-06 ***
## marksspring -3.957121e-02 5.053363e-02 -1.386153e-01 5.947288e-02
## markssummer 7.891398e-01 4.266227e-02 7.055233e-01 8.727563e-01 ***
## markswinter -2.379296e+00 1.215116e-01 -2.617454e+00 -2.141137e+00 ***
## Zval
## (Intercept) -397.7247657
## elev -38.0729907
## I(elev^2) 15.4787625
## marksspring -0.7830669
## markssummer 18.4973701
## markswinter -19.5808065
# Compares models using AIC
cat("AIC for poly model: ", AIC(model_poly_elevation), "\n")
## AIC for poly model: 142038.1
cat("AIC for gam model: ", AIC(gam_elevation), "\n")
## AIC for gam model: 4186.001
# Creates seasonal ppp objects
ppp_list <- list()
for (s in names(seasons)) {
bears_loc_season <- bears_loc_filtered[bears_loc_filtered$month %in% seasons[[s]], ]
bears_sf_season <- st_as_sf(bears_loc_season, coords = c("decimalLongitude", "decimalLatitude"), crs = 4326)
bears_sf_season_proj <- st_transform(bears_sf_season, crs = 3005)
coords_season <- st_coordinates(bears_sf_season_proj)
suppressWarnings(
ppp_list[[s]] <- ppp(x = coords_season[,1], y = coords_season[,2], window = window)
)
}
# Extracts covariates
elevation <- DATA$Elevation
cover <- DATA$Forest
hfi <- DATA$HFI
dist_water <- DATA$Dist_Water
# KDE Surface Comparison
dens_list <- lapply(ppp_list, function(p) density(p, sigma = 10000))
for (s in names(dens_list)) {
plot(dens_list[[s]], main = paste("KDE Surface -", s))
}
# quadrat tests
for (s in names(ppp_list)) {
qt <- quadrat.test(ppp_list[[s]], nx = 5, ny = 5)
print(qt)
plot(qt, main = paste("Quadrat test -", s))
}
## Warning: Some expected counts are small; chi^2 approximation may be inaccurate
##
## Chi-squared test of CSR using quadrat counts
##
## data: ppp_list[[s]]
## X2 = 561.39, df = 20, p-value < 2.2e-16
## alternative hypothesis: two.sided
##
## Quadrats: 21 tiles (irregular windows)
## Warning: Some expected counts are small; chi^2 approximation may be inaccurate
##
## Chi-squared test of CSR using quadrat counts
##
## data: ppp_list[[s]]
## X2 = 2202.7, df = 20, p-value < 2.2e-16
## alternative hypothesis: two.sided
##
## Quadrats: 21 tiles (irregular windows)
## Warning: Some expected counts are small; chi^2 approximation may be inaccurate
##
## Chi-squared test of CSR using quadrat counts
##
## data: ppp_list[[s]]
## X2 = 3767, df = 20, p-value < 2.2e-16
## alternative hypothesis: two.sided
##
## Quadrats: 21 tiles (irregular windows)
## Warning: Some expected counts are small; chi^2 approximation may be inaccurate
##
## Chi-squared test of CSR using quadrat counts
##
## data: ppp_list[[s]]
## X2 = 2720.5, df = 20, p-value < 2.2e-16
## alternative hypothesis: two.sided
##
## Quadrats: 21 tiles (irregular windows)
# inhomogeneous poission model
for (s in names(ppp_list)) {
model <- ppm(ppp_list[[s]] ~ elev, covariates = list(elev = elevation))
plot(predict(model), main = paste("Intensity ~ Elevation -", s))
}
## Warning: glm.fit: algorithm did not converge
## Warning: Values of the covariate 'elev' were NA or undefined at 0.02% (1 out of
## 5456) of the quadrature points. Occurred while executing: ppm.ppp(Q =
## ppp_list[[s]], trend = ~elev, data = NULL, interaction = NULL,
# multivariate ppm
for (s in names(ppp_list)) {
model <- ppm(ppp_list[[s]] ~ elev + cover + hfi + dist_water,
covariates = list(elev = elevation, cover = cover, hfi = hfi, dist_water = dist_water))
print(summary(model))
plot(predict(model), main = paste("Predicted Intensity -", s))
}
## Warning: Values of the covariate 'hfi' were NA or undefined at 0.68% (4 out of
## 587) of the quadrature points. Occurred while executing: ppm.ppp(Q =
## ppp_list[[s]], trend = ~elev + cover + hfi + dist_water,
## Warning: glm.fit: algorithm did not converge
## Point process model
## Fitted to data: ppp_list[[s]]
## Fitting method: maximum likelihood (Berman-Turner approximation)
## Model was fitted using glm()
## *** Algorithm did not converge ***
## Call:
## ppm.formula(Q = ppp_list[[s]] ~ elev + cover + hfi + dist_water,
## covariates = list(elev = elevation, cover = cover, hfi = hfi,
## dist_water = dist_water))
## Edge correction: "border"
## [border correction distance r = 0 ]
## --------------------------------------------------------------------------------
## Quadrature scheme (Berman-Turner) = data + dummy + weights
##
## Data pattern:
## Planar point pattern: 74 points
## Average intensity 7.8e-11 points per square unit
## Window: polygonal boundary
## 378 separate polygons (2 holes)
## vertices area relative.area
## polygon 1 5454 889865000000 9.38e-01
## polygon 2 19 11135700 1.17e-05
## polygon 3 6 1679950 1.77e-06
## polygon 4 59 375017000 3.95e-04
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## polygon 6 5 1220870 1.29e-06
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## (1597000 x 1367000 units)
## Window area = 9.48262e+11 square units
## Fraction of frame area: 0.435
## Quadrature weights:
## (counting weights based on 32 x 32 array of rectangular tiles)
## All weights:
## range: [55500000, 2.13e+09] total: 9.47e+11
## Weights on data points:
## range: [59300000, 1.07e+09] total: 2.75e+10
## Weights on dummy points:
## range: [55500000, 2.13e+09] total: 9.2e+11
## --------------------------------------------------------------------------------
## FITTED :
##
## Nonstationary Poisson process
##
## ---- Intensity: ----
##
## Log intensity: ~elev + cover + hfi + dist_water
## Model depends on external covariates 'elev', 'cover', 'hfi' and 'dist_water'
## Covariates provided:
## elev: im
## cover: im
## hfi: im
## dist_water: im
##
## Fitted trend coefficients:
## (Intercept) elev cover hfi dist_water
## -2.345970e+01 -3.511481e-03 1.690825e-02 4.869412e+00 9.553740e-05
##
## Estimate S.E. CI95.lo CI95.hi Ztest
## (Intercept) -2.345970e+01 5.287726e-01 -2.449607e+01 -22.423323608 ***
## elev -3.511481e-03 4.743760e-04 -4.441241e-03 -0.002581722 ***
## cover 1.690825e-02 5.095351e-03 6.921542e-03 0.026894951 ***
## hfi 4.869412e+00 5.529194e-01 3.785710e+00 5.953114352 ***
## dist_water 9.553740e-05 5.890243e-05 -1.990924e-05 0.000210984
## Zval
## (Intercept) -44.366332
## elev -7.402317
## cover 3.318367
## hfi 8.806731
## dist_water 1.621960
##
## ----------- gory details -----
##
## Fitted regular parameters (theta):
## (Intercept) elev cover hfi dist_water
## -2.345970e+01 -3.511481e-03 1.690825e-02 4.869412e+00 9.553740e-05
##
## Fitted exp(theta):
## (Intercept) elev cover hfi dist_water
## 6.480108e-11 9.964947e-01 1.017052e+00 1.302443e+02 1.000096e+00
## Problem:
## Values of the covariate 'hfi' were NA or undefined at 0.68% (4 out of 587) of the quadrature points
## Warning: Values of the covariate 'hfi' were NA or undefined at 0.45% (12 out of
## 2667) of the quadrature points. Occurred while executing: ppm.ppp(Q =
## ppp_list[[s]], trend = ~elev + cover + hfi + dist_water,
## Point process model
## Fitted to data: ppp_list[[s]]
## Fitting method: maximum likelihood (Berman-Turner approximation)
## Model was fitted using glm()
## Algorithm converged
## Call:
## ppm.formula(Q = ppp_list[[s]] ~ elev + cover + hfi + dist_water,
## covariates = list(elev = elevation, cover = cover, hfi = hfi,
## dist_water = dist_water))
## Edge correction: "border"
## [border correction distance r = 0 ]
## --------------------------------------------------------------------------------
## Quadrature scheme (Berman-Turner) = data + dummy + weights
##
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## (1597000 x 1367000 units)
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## Fraction of frame area: 0.435
##
## Dummy quadrature points:
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## dummy spacing: 24948.41 x 21353.49 units
##
## Original dummy parameters: =
## Planar point pattern: 1899 points
## Average intensity 2e-09 points per square unit
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## enclosing rectangle: [273874.9, 1870573.4] x [369042.8, 1735666.4] units
## (1597000 x 1367000 units)
## Window area = 9.48262e+11 square units
## Fraction of frame area: 0.435
## Quadrature weights:
## (counting weights based on 64 x 64 array of rectangular tiles)
## All weights:
## range: [6750000, 5.33e+08] total: 9.45e+11
## Weights on data points:
## range: [6750000, 2.92e+08] total: 6.97e+10
## Weights on dummy points:
## range: [6750000, 5.33e+08] total: 8.75e+11
## --------------------------------------------------------------------------------
## FITTED :
##
## Nonstationary Poisson process
##
## ---- Intensity: ----
##
## Log intensity: ~elev + cover + hfi + dist_water
## Model depends on external covariates 'elev', 'cover', 'hfi' and 'dist_water'
## Covariates provided:
## elev: im
## cover: im
## hfi: im
## dist_water: im
##
## Fitted trend coefficients:
## (Intercept) elev cover hfi dist_water
## -2.111907e+01 -1.478995e-03 9.975132e-03 4.838300e+00 -3.936119e-05
##
## Estimate S.E. CI95.lo CI95.hi Ztest
## (Intercept) -2.111907e+01 1.352834e-01 -2.138422e+01 -2.085392e+01 ***
## elev -1.478995e-03 9.298462e-05 -1.661242e-03 -1.296749e-03 ***
## cover 9.975132e-03 1.304182e-03 7.418982e-03 1.253128e-02 ***
## hfi 4.838300e+00 1.561870e-01 4.532179e+00 5.144421e+00 ***
## dist_water -3.936119e-05 2.095225e-05 -8.042685e-05 1.704473e-06
## Zval
## (Intercept) -156.109836
## elev -15.905807
## cover 7.648573
## hfi 30.977604
## dist_water -1.878614
##
## ----------- gory details -----
##
## Fitted regular parameters (theta):
## (Intercept) elev cover hfi dist_water
## -2.111907e+01 -1.478995e-03 9.975132e-03 4.838300e+00 -3.936119e-05
##
## Fitted exp(theta):
## (Intercept) elev cover hfi dist_water
## 6.731366e-10 9.985221e-01 1.010025e+00 1.262546e+02 9.999606e-01
## Problem:
## Values of the covariate 'hfi' were NA or undefined at 0.45% (12 out of 2667) of the quadrature points
## Warning: Values of the covariates 'elev', 'hfi' were NA or undefined at 0.4%
## (22 out of 5456) of the quadrature points. Occurred while executing: ppm.ppp(Q
## = ppp_list[[s]], trend = ~elev + cover + hfi + dist_water,
## Point process model
## Fitted to data: ppp_list[[s]]
## Fitting method: maximum likelihood (Berman-Turner approximation)
## Model was fitted using glm()
## Algorithm converged
## Call:
## ppm.formula(Q = ppp_list[[s]] ~ elev + cover + hfi + dist_water,
## covariates = list(elev = elevation, cover = cover, hfi = hfi,
## dist_water = dist_water))
## Edge correction: "border"
## [border correction distance r = 0 ]
## --------------------------------------------------------------------------------
## Quadrature scheme (Berman-Turner) = data + dummy + weights
##
## Data pattern:
## Planar point pattern: 1759 points
## Average intensity 1.85e-09 points per square unit
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## enclosing rectangle: [273874.9, 1870573.4] x [369042.8, 1735666.4] units
## (1597000 x 1367000 units)
## Window area = 9.48262e+11 square units
## Fraction of frame area: 0.435
## Quadrature weights:
## (counting weights based on 90 x 90 array of rectangular tiles)
## All weights:
## range: [2760000, 2.69e+08] total: 9.45e+11
## Weights on data points:
## range: [2760000, 1.35e+08] total: 8.26e+10
## Weights on dummy points:
## range: [2760000, 2.69e+08] total: 8.63e+11
## --------------------------------------------------------------------------------
## FITTED :
##
## Nonstationary Poisson process
##
## ---- Intensity: ----
##
## Log intensity: ~elev + cover + hfi + dist_water
## Model depends on external covariates 'elev', 'cover', 'hfi' and 'dist_water'
## Covariates provided:
## elev: im
## cover: im
## hfi: im
## dist_water: im
##
## Fitted trend coefficients:
## (Intercept) elev cover hfi dist_water
## -2.046112e+01 -1.310042e-03 1.045653e-02 4.990537e+00 -3.885610e-05
##
## Estimate S.E. CI95.lo CI95.hi Ztest
## (Intercept) -2.046112e+01 9.180183e-02 -2.064105e+01 -2.028120e+01 ***
## elev -1.310042e-03 6.134897e-05 -1.430284e-03 -1.189800e-03 ***
## cover 1.045653e-02 8.686491e-04 8.754013e-03 1.215906e-02 ***
## hfi 4.990537e+00 1.087027e-01 4.777484e+00 5.203591e+00 ***
## dist_water -3.885610e-05 1.341862e-05 -6.515611e-05 -1.255610e-05 **
## Zval
## (Intercept) -222.883618
## elev -21.353940
## cover 12.037696
## hfi 45.909988
## dist_water -2.895686
##
## ----------- gory details -----
##
## Fitted regular parameters (theta):
## (Intercept) elev cover hfi dist_water
## -2.046112e+01 -1.310042e-03 1.045653e-02 4.990537e+00 -3.885610e-05
##
## Fitted exp(theta):
## (Intercept) elev cover hfi dist_water
## 1.299710e-09 9.986908e-01 1.010511e+00 1.470154e+02 9.999611e-01
## Problem:
## Values of the covariates 'elev', 'hfi' were NA or undefined at 0.4% (22 out of 5456) of the quadrature points
## Warning: Values of the covariate 'hfi' were NA or undefined at 0.67% (18 out of
## 2698) of the quadrature points. Occurred while executing: ppm.ppp(Q =
## ppp_list[[s]], trend = ~elev + cover + hfi + dist_water,
## Point process model
## Fitted to data: ppp_list[[s]]
## Fitting method: maximum likelihood (Berman-Turner approximation)
## Model was fitted using glm()
## Algorithm converged
## Call:
## ppm.formula(Q = ppp_list[[s]] ~ elev + cover + hfi + dist_water,
## covariates = list(elev = elevation, cover = cover, hfi = hfi,
## dist_water = dist_water))
## Edge correction: "border"
## [border correction distance r = 0 ]
## --------------------------------------------------------------------------------
## Quadrature scheme (Berman-Turner) = data + dummy + weights
##
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## Average intensity 8.43e-10 points per square unit
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##
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##
## Original dummy parameters: =
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## (1597000 x 1367000 units)
## Window area = 9.48262e+11 square units
## Fraction of frame area: 0.435
## Quadrature weights:
## (counting weights based on 64 x 64 array of rectangular tiles)
## All weights:
## range: [5180000, 5.33e+08] total: 9.45e+11
## Weights on data points:
## range: [5180000, 2.66e+08] total: 6.3e+10
## Weights on dummy points:
## range: [7240000, 5.33e+08] total: 8.82e+11
## --------------------------------------------------------------------------------
## FITTED :
##
## Nonstationary Poisson process
##
## ---- Intensity: ----
##
## Log intensity: ~elev + cover + hfi + dist_water
## Model depends on external covariates 'elev', 'cover', 'hfi' and 'dist_water'
## Covariates provided:
## elev: im
## cover: im
## hfi: im
## dist_water: im
##
## Fitted trend coefficients:
## (Intercept) elev cover hfi dist_water
## -2.059377e+01 -2.172077e-03 8.193666e-03 4.581051e+00 -6.675436e-05
##
## Estimate S.E. CI95.lo CI95.hi Ztest
## (Intercept) -2.059377e+01 1.402255e-01 -2.086860e+01 -2.031893e+01 ***
## elev -2.172077e-03 1.008390e-04 -2.369717e-03 -1.974436e-03 ***
## cover 8.193666e-03 1.428951e-03 5.392973e-03 1.099436e-02 ***
## hfi 4.581051e+00 1.520399e-01 4.283058e+00 4.879044e+00 ***
## dist_water -6.675436e-05 2.184644e-05 -1.095726e-04 -2.393613e-05 **
## Zval
## (Intercept) -146.861800
## elev -21.540041
## cover 5.734042
## hfi 30.130590
## dist_water -3.055617
##
## ----------- gory details -----
##
## Fitted regular parameters (theta):
## (Intercept) elev cover hfi dist_water
## -2.059377e+01 -2.172077e-03 8.193666e-03 4.581051e+00 -6.675436e-05
##
## Fitted exp(theta):
## (Intercept) elev cover hfi dist_water
## 1.138259e-09 9.978303e-01 1.008227e+00 9.761692e+01 9.999332e-01
## Problem:
## Values of the covariate 'hfi' were NA or undefined at 0.67% (18 out of 2698) of the quadrature points
# Ripley's K with Envelope for each season
for (s in names(ppp_list)) {
# Compute Ripley's K for the current season
K <- Kest(ppp_list[[s]])
E <- envelope(ppp_list[[s]],
Kest,
correction = "border",
rank = 1,
nsim = 19,
fix.n = TRUE)
plot(K,
main = paste("Ripley's K -", s))
plot(E,
add = TRUE,
lty = 2)
}
## Generating 19 simulations of CSR with fixed number of points ...
## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
## 19.
##
## Done.
## Generating 19 simulations of CSR with fixed number of points ...
## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
## 19.
##
## Done.
## Generating 19 simulations of CSR with fixed number of points ...
## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
## 19.
##
## Done.
## Generating 19 simulations of CSR with fixed number of points ...
## 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18,
## 19.
##
## Done.